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出版社:世界圖書出版公司
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ISBN:9787510054020
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作者:(德)喬治,H-O
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頁數:545
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出版日期:2017-01-01
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印刷日期:2017-01-01
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包裝:平裝
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開本:16開
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版次:1
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印次:1
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字數:672千字
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喬治,H-O著的《吉布斯測度和相變(第2版)(英文 版)》不僅僅是對吉布斯測度和相變的一個簡單的介紹 ,其中還包括統計力學下相變中的數學理論和廣泛而 具有深度的討論。本書主要包括四部分,第一部分是 理論的基本理論;第二部分是對經典理論一繫列結果 的總結;第三部分是在Zd上的空間分布均勻的吉布斯 測度;第四部分是基於Zd移位不變性模型的相位變化 的存在性。讀者對像:數學和理論物理領域的研究生 和科研工作者。
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Introduction Part Ⅰ. General theory and basic examples Chapter 1 Specifications of random fields 1.1 Preliminaries 1.2 Prescribing conditional probabilities 1.3 A-specifications Chapter 2 Gibbsian specifications 2.1 Potentials 2.2 Quasilocality 2.3 Gibbs representation of pre-modifications 2.4 Equivalence of potentials Chapter 3 Finite state Markov chains as Gibbs measures 3.1 Markov specifications on the integers 3.2 The one-dimensional Ising model 3.A Appendix. Positive matrices Chapter 4 The existence problem 4.1 Local convergence of random fields 4.2 Existence of cluster points 4.3 Continuity results 4.4 Existence and topological properties of Gibbs measures 4.A Appendix. Standard Borel spaces Chapter 5 Specifications with symmetries 5.1 Transformations of specifications 5.2 Gibbs measures with symmetries Chapter 6 Three examples of symmetry breaking 6.1 Inhomogeneous Ising chains 6.2 The Ising ferromagnet in two dimensions 6.3 Shlosman's random staircases Chapter 7 Extreme Gibbs measures 7.1 Tail triviality and approximation 7.2 Some applications 7.3 Extreme decomposition 7.4 Macroscopic equivalence of Gibbs simplices Chapter 8 Uniqueness 8.1 Dobrushin's condition of weak dependence 8.2 Further consequences of Dobrushin's condition 8.3 Uniqueness in one dimension Chapter 9 Absence of symmetry breaking. Non-existence 9.1 Discrete symmetries in one dimension 9.2 Continuous symmetries in two dimensions Part Ⅱ. Markov chains and Gauss fields as Gibbs measures Chapter 10 Markov fields on the integers I 10.1 Two-sided and one-sided Markov property 10.2 Markov fields which are Markov chains 10.3 Uniqueness of the shift-invariant Markov field Chapter 11 Markov fields on the integers II 11.1 Boundary laws, uniqueness, and non-existence 11.2 The Spitzer-Cox example of phase transition 11.3 Kalikow's example of phase transition 11.4 Spitzer's example of totally broken shift-invariance Chapter 12 Markov fields on trees 12.1 Markov chains and boundary laws 12.2 The Ising model on Cayley trees Chapter 13 Gaussian fields 13.1 Gauss fields as Gibbs measures 13.2 Gibbs measures for Gaussian specifications 13.3 The homogeneous case 13.A Appendix. Some tools of Gaussian analysis Part Ⅲ. Shift-invariant Gibbs measures Chapter 14 Ergodicity 14.1 Ergodic random fields 14.2 Ergodic Gibbs measures 14.A Appendix. The multidimensional ergodic theorem Chapter 15 The specific free energy and its minimization I5.I Relative entropy 15.2 Specific entropy 15.3 Specific energy and free energy 15.4 The variational principle 15.5 Large deviations and equivalence of ensembles Chapter 16 Convex geometry and the phase diagram 16.1 The pressure and its tangent functionals 16.2 A geometric view of Gibbs measures 16.3 Phase transitions with prescribed order parameters 16.4 Ubiquity of pure phases Part Ⅳ. Phase transitions in reflection positive models Chapter 17 Reflection positivity 17.1 The chessboard estimate 17.2 Gibbs distributions with periodic boundary condition Chapter 18 Low energy oceans and discrete symmetry breaking 18.1 Percolation of spin patterns 18.2 Discrete symmetry breaking at low temperatures 18.3 Examples Chapter 19 Phase transitions without symmetry breaking 19.1 Potentials with degenerated ground states, and perturbations thereof 19.2 Exploiting Sperner's lemma 19.3 Models with an entropy-energy conflict 19.A Appendix. Sperner's lemma Chapter 20 Continuous symmetry breaking in N-vector models 20.1 Some preliminaries 20.2 Spin wave analysis, and spontaneous magnetization Bibliographical Notes Further Progress References References to the Second Edition List of Symbols Index
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